BROWNIAN MODELS OF CLOSED QUEUEING NETWORKS: EXPLICIT SOLUTIONS FOR BALANCED THREE-STATION SYSTEMS
成果类型：
Article
署名作者：
Schwerer, Elizabeth; Van Mieghem, Jan A.
署名单位：
Stanford University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177005068
发表日期：
1994
页码：
448-477
关键词：
摘要：
We study a closed, three-station queueing network with general service time distributions and balanced workloads (that is, each station has the same relative traffic intensity). If the customer population is large, then the queue length process of such a network can be approximated by driftless reflected Brownian motion (RBM) in a simplex. Building on earlier work by Harrison, Landau and Shepp, we develop explicit formulas for various quantities associated with the stationary distribution of RBM in a general triangle and use them to derive approximate performance measures for the closed queueing network. In particular, we develop approximations for the throughput rate and for moments and tail fractiles of the throughput time distribution. Also, crude bounds on the throughput rate and mean throughput time are proposed. Finally, we present three examples that test the accuracy of both the Brownian approximation and our performance estimates.